Optic flow calculations with nonlinear smoothness terms extended into the temporal domain

Non-quadratic variational regularization is a well known and powerful approach for the discontinuity-preserving computation of optical flow. In the present paper, we introduce an extension of nonlinear spatial smoothness terms to nonlinear spatio-temporal and flow-driven regularization. To assess the performance of our approach, the implementation is purely based on the corresponding reaction-diffusion system and dispenses with any pre-smoothing typically used for canceling out noise and estimating partial derivatives. Results for real-world scenes show that our spatio-temporal approach (i) improves optical flow fields significantly, (ii) smoothes out background noise efficiently, and (iii) enhances true motion boundaries. The computational costs required are only twice as high as with a pure 2D spatial approach